PIRSA:12040116

A Monomial Matrix Formalism to Describe Quantum Many-body States

Van den Nest, M. (2012). A Monomial Matrix Formalism to Describe Quantum Many-body States. Perimeter Institute. https://pirsa.org/12040116

Van den Nest, Maarten. A Monomial Matrix Formalism to Describe Quantum Many-body States. Perimeter Institute, Apr. 16, 2012, https://pirsa.org/12040116 

          @misc{ pirsa_PIRSA:12040116,
            doi = {10.48660/12040116},
            url = {https://pirsa.org/12040116},
            author = {Van den Nest, Maarten},
            keywords = {Quantum Information},
            language = {en},
            title = {A Monomial Matrix Formalism to Describe Quantum Many-body States},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {apr},
            note = {PIRSA:12040116 see, \url{https://pirsa.org}}
          }

Maarten Van den Nest Universität Innsbruck

Talk numberPIRSA:12040116
DOI10.48660/12040116
Collection
Talk Type Scientific Series
Subject

Abstract

We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called "M-spaces"; a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the AKLT model, Kitaev's anyon models, W states and several others. We furthermore demonstrate how basic properties of M-spaces can transparently be understood by manipulating their monomial stabilizer groups. Finally we show that a large subclass of M-spaces can be simulated efficiently classically with one unified method. [cf. M. Van den Nest, http://arxiv.org/abs/1108.0531]